This paper surveys results of the authors and others conceming estimates for the Hausdorff
dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and …

This book deals with the investigation of global attractors of nonlinear dynamical systems.
The exposition proceeds from the simplest attractor of a single equilibrium to more …

In this book, we continue the investigations of global attractors and invariant sets for
dynamical systems by means of Lyapunov functions and adapted metrics. The effectiveness …

Along with widely used numerical methods for estimating and computing the Lyapunov
dimension there is an effective analytical approach, proposed by GA Leonov in 1991. The …

RA Smith [19] showed that his higher dimensional generalization of Bendixson's criterion for
the nonexistence of periodic solutions to an autonomous differential equation implies that all …

The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of
parameters, including classical values, was analytically obtained first by GA Leonov in 2002 …

Frequency estimates are derived for the Lyapunov dimension of attractors of non-linear
dynamical systems. A theorem on the localization of global attractors is proved for the …

When a deterministic mechanism gives rise to an erratic time series, then under certain
conditions the series is said to exhibit chaos. The catalogue of statistical methods for the …

In this paper, a new bound on the trajectories of the Lorenz system is derived. This result is
useful to show that the transverse stability of the origin in two Lorenz systems coupled in a …

Dieses Lehrbuch basiert auf Ausarbeitungen zu verschiedenen Vorlesungen, die ich in den
Jahren 1989 bis 1996 an der TU Dresden gehalten habe. Zu den Hörern dieser …